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x+1","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:                1936,                2112,                  576;\n  1:               85184,              139392,                76032,                13824;\n  2:             3748096,             8177664,              6690816,              2433024,               331776;\n  3:           164916224,           449771520,            490659840,            267632640,             72990720,              7962624;\n  4:          7256313856,         23747936256,          32383549440,          23551672320,           9634775040,           2102132736,            191102976;\n  5:        319277809664,       1219060727808,        1994826645504,        1813478768640,         989170237440,         323728441344,          58859716608,          4586471424;\n  6:      14048223625216,      61301339455488,      117029829869568,      127668905312256,       87046980894720,       37984137117696,       10359310123008,       1614437941248,        110075314176;\n  7:     618121839509504,    3034416303046656,     6620544661192704,     8426147750608896,     6894120886861824,     3760429574651904,     1367428936237056,     319658712367104,      43589824413696,      2641807540224;\n  8:   27197360938418176,  148349241482280960,   364129956365598720,   529643572895416320,   505568865036533760,   330917802569367552,   150417182986076160,   46883277813841920,    9589761371013120,   1162395317698560,    63403380965376;\n  9: 1196683881290399744, 7180103287742398464, 19582099875661086720, 32043436160172687360, 34956475811097477120, 26694036073928982528, 14560383313052172288, 5672876615474872320, 1547148167856783360, 281299666883051520, 30687236387241984, 1521681143169024;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (44+24*x)*P(n-1,x) for n >= 1, with P(0,x) = 1936 + 2112*x + 576*x^2.","mathematica":"P[0, x_] := 1936 + 2112*x + 576*x^2;\nP[n_, x_] := P[n, x] = Expand[(44 + 24*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1936 + 2112*x + 576*x^2; for(n = 1, N, my(i = n + 1); v[i] = (44 + 24*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-6874f381e9c7e0a2","steps":["basis A013610","basis A007318"],"edges":["e-889e30cc3b49f76a","e-57f28868c68f1b7f"],"text":"A038334 \u2192 basis A013610 \u2192 basis A007318"},"headline":"A038334 \u2192 basis A013610 \u2192 basis A007318","chain":null}